Getal & Ruimte (12e editie) - vwo wiskunde B
'Rekenen met logaritmen'.
| vwo wiskunde B | 5.4 Logaritmen |
opgave 1Bereken. 1p a \({}^{7}\!\log(49)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{7}\!\log(49) = {}^{7}\!\log(7^{2}) = 2\) 1p 1p b \({}^{3}\!\log(3)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{3}\!\log(3) = {}^{3}\!\log(3^{1}) = 1\) 1p 1p c \(\log(1\,000\,000)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(1\,000\,000) = \log(10^{6}) = 6\) 1p 1p d \({}^{7}\!\log(\frac{1}{7})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{7}\!\log(\frac{1}{7}) = {}^{7}\!\log(7^{-1}) = -1\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{4}}\!\log(\frac{1}{16})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{4}}\!\log(\frac{1}{16}) = {}^{\frac{1}{4}}\!\log(\frac{1}{4}^{2}) = 2\) 1p 1p b \({}^{\frac{1}{5}}\!\log(25)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{5}}\!\log({}^{\frac{1}{5}}\!\log(25)) = {}^{\frac{1}{5}}\!\log(\frac{1}{5}^{-2}) = -2\) 1p 1p c \({}^{2}\!\log(8 \sqrt{2})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{2}\!\log(8 \sqrt{2}) = {}^{2}\!\log(2^{3} ⋅ 2^{\frac{1}{2}}) = {}^{2}\!\log(2^{3\frac{1}{2}}) = 3\frac{1}{2}\) 1p 1p d \({}^{6}\!\log(6^{1{,}9})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{6}\!\log(6^{1{,}9}) = 1{,}9\) 1p |